HDFS 2900 Spring 2015 Dr Feng Study Guide for Exam 3 Quantitative Data Analysis Chapter 8 Descriptive statistics statistics used to describe the distribution of and relationships among variables o Central tendency the most common value for variables measured at the nominal level or the value around which cases tend to center for a quantitative variable o Variability variation the extent to which cases are spread out through the distribution or clustered around just one value o Skewness the extent to which cases are clustered more at one or the other end of the distribution of a quantitative variable rather than in a symmetric pattern around its center Skew can be positive to the right with numbers tapering in a positive direction or negative with number tapering off in negative direction o Know how to interpret graphs i e histogram bar graph and line graph o Measures for central tendency Central tendency is summarized with one of three statistics Mode most frequent value in a distribution also termed probability average Median position average that divides a distribution in half the 50th percentile Mean The arithmetic or weighted average computed by adding up the value of all the cases and dividing by the total number of cases o Measures of variation Captures how widely and densely spread the numbers are Range the true upper limit in a distribution minus the true lower limit or the highest rounded value minus the lowest rounded value plus 1 Interquartile range The range in a distribution between the end of the 1st quartile and the beginning of the 3rd quartile Variance A statistic that measures the variability of a distribution as the average squared deviation of each case from the mean Standard deviation distance from the mean that covers a clear majority of cases about 2 3 It is the square root of the variance o Which central tendency statistics and which variability statistics are appropriate under what conditions Mode Most appropriate for nominal data Can easily give a misleading impression of a distribution s central tendency Problems occur with bimodal distributions 2 categories with roughly equal numbers of cases and clearly more cases that the other categories However it can be used to characterize central tendency of variables at the nominal level Because it is the most probable value it can be used to answer questions such as which ethnic group is most common in a given school Median For ordered data Not appropriate for variables that are measured at the nominal level their values cannot be put in order so there is no meaningful middle position Mean For interval and ratio data Only makes sense if the values of the cases can be treated as actual quantities That is if they reflect an interval or ratio level of measurement or if we assume that an ordinal measure can be treated as an interval Should not measure qualitative variables such as religion Range Not a good summary measure since outliers can alter it drastically It is to identify the whole range of possible values that might be encountered Interquartile range avoids problem outliers and shows the range where most cases lie Variance mainly used to compute standard deviation Conventionally used to measure variability with the closely related SD than with the variance HDFS 2900 Spring 2015 Dr Feng Standard deviation preferred measure of variability particularly when a variable is normally distributed It can tell you quickly about how wide the variation is of any set of cases or the range in which most cases will fall The normal curve symmetric distribution shaped like a bell and centered around the population mean Inferential statistics and hypothesis testing o Inferential stats Estimate the degree of confidence that can be placed in generalizations from a sample to the population o Null hypothesis Statement of no association or no difference Ex There is no difference between male and female students on number of Facebook friends o Alternative hypothesis Statement that there is an association between variables or there is a difference between groups Ex1 Male and female students differ on the number of Facebook friends they have nondirectional Ex2 Male students have more Facebook friends than female students directional o Statistical significance what does the p value mean The mathematical likelihood that an association is not due to chance judged by a criterion the analyst sets Basically concludes a relationship exists Often the probability is less than 5 out of 100 or p 05 If the p value is less than 05 p 05 the possibility of the null hypothesis being true is very small We reject the null hypothesis and accept the alternative hypothesis We conclude that the association or group difference found is statistically significant Association between variables o Chi square an inferential statistic used to test hypthesses about relationships between two or more variables in cross tabulation Customarily reported in a summary form such as p 05 which can be translated as probability that the association was due to chance is less than 5 out of 100 Association between variables measured at nominal or ordinal level Example Is gender associated with frequency of Facebook profiles update Null hypothesis no association o Correlation Alternative hypothesis there is an association or females updates their Facebook profiles more frequently than males Association between variables measured at interval or ratio level Correlation between two variables ranges from 1 to 1 Close to 1 or 1 strong correlation Close to 0 no correlation Is extraversion related to number of Facebook photos The correlation analysis shows r 37 p 04 We reject the null hypothesis and conclude that students who are more extraverted Comparing groups t test have more Facebook friends o Difference in means between two groups o t the ratio of difference between the group means and the variability within groups o Do males and females differ in number of facebook photos o Null hypothesis Males and females do not differ o Alternative hypothesis Males and females differ in number of facebook photos HDFS 2900 Spring 2015 Dr Feng o Females have more facebook photos than males o Results of t test indicate that t 3 15 p 004 o Thus we reject the null hypothesis and conclude that difference between males and females are statistically significant females have more facebook photos than males Qualitative Data Analysis Chapters 9 10 class notes Common features of qualitative methods o